Physiologically Structured Population Models: Towards a General Mathematical Theory
Authors: Diekmann O, Gyllenberg M, Metz JAJ
Publication Year: 2007
Reference: IIASA Interim Report IR-07-046
Abstract
We review the state-of-the-art concerning a mathematical framework for general physiologically structured population models. When individual development is affected by the population density, such models lead to quasilinear equations. We show how to associate a dynamical system (defined on an infinite dimensional state space) to the model and how to determine the steady states. Concerning the principle of linearized stability, we offer a conjecture as well as some preliminary steps towards a proof.